What is the probability that a random integral quadratic form in nn variables has an integral zero?

We show that the density of quadratic forms in $n$ variables over $\mathbb Z_p$ that are isotropic is a rational function of $p$, where the rational function is independent of $p$, and we determine this rational function explicitly. When real quadratic forms in $n$ variables are distributed according to the Gaussian Orthogonal Ensemble (GOE) of random matrix theory, we determine explicitly the probability that a random such real quadratic form is isotropic (i.e., indefinite). As a consequence, for each $n$, we determine an exact expression for the probability that a random integral quadratic form in $n$ variables is isotropic (i.e., has a nontrivial zero over $\mathbb Z$), when these integral quadratic forms are chosen according to the GOE distribution. In particular, we find an exact expression for the probability that a random integral quaternary quadratic form has an integral zero; numerically, this probability is approximately $98.3\%$.Comment: 17 pages. This article supercedes arXiv:1311.554

Molecular approaches towards assessment of cyanobacterial biodiversity

No Abstrac

Chemistry of Metal (Benzylidene) Picramate-Part III Benzylidene Picramates of Zinc Cadmium and Mercury

Benzylidene picramates of zinc, cadmium and mercury have been prepared by treating the corresponding aqueous sulphate and chloride solutions with sodium salt of 4'-dimethylaminobenzylidence-2-hydroxy-3, 5-dinitroaniline. A metal: ligand ratio of 1:2 has been established in all these cases. I.R. spectral studies of metal benzylidene picramates show N-M coordination (where M is zinc, cadmium or mercury). Explosive properties of these benzylidene picramates have also been studied and it was found that the thermal stability increases as the atomic radius decreases or ionization potential increases

The BG News November 28, 2012

The BGSU campus student newspaper November 28, 2012. Volume 103 - Issue 43https://scholarworks.bgsu.edu/bg-news/9579/thumbnail.jp

Ni/H-ZSM-5 as a stable and promising catalyst for COx free H2 production by CH4 decomposition

Catalytic decomposition of methane for COx free hydrogen production is carried out over Ni supported on H-ZSM-5 catalysts with different Si/Al ratios (i.e. 40, 150, 300 and 485) at 550 °C and atmospheric pressure. Methane decomposition activity of Ni/H-ZSM-5 is decreased with time on stream and finally deactivated completely. The fresh and reduced catalysts are characterized by BET-SA, XRD, FT-IR, UV-DRS, TPR, pulse chemisorption of H2 and N2O and some of the used catalysts are characterised by CHNS, SEM, TEM and Raman spectroscopy. Raman spectra of the used catalysts showed both ordered and disordered carbon at 1580 cm-1 and 1320 cm-1. The 20 wt% Ni/H-ZSM-5 (Si/Al = 150) exhibited a higher H2 production rate over the other Ni loadings. The superior performance of 20 wt% Ni/H-ZSM-5 (Si/Al = 150) is rationalized by the physico-chemical properties of the various Ni loaded H-ZSM-5 catalysts

Salinity and Toxicological Studies of Waters of Rajasthan Desert

Detailed studies on quality of ground waters of Western Rajasthan have been carried out by analysing about 1500 water samples for presence of total dissolved solids (TDS) and other normal chemical constituents. 109 ground water samples were tested for presence of 8 toxic substances viz. As, Ba, Cd, Cr/sup +6/, Pb, Se, Ag, and CN and F and NO/sub 3/. About 9 percent of the waters conform to the normal standards of drinking water i.e. contain less than 500 mg/l TDS. None of the water points has been found to be contaminated with toxic substances. However, fluoride and nitrate were present in all the samples.A survey of water-borne diseases, kidney diseases and fluorosis carried out to establish the possible correlation between prevailing diseases and dissolved solids in waters indicate that 82 percent of the reported cases are due to water-borne diseases. The guinea-worm (Dracunculus medinensis) has been found in the surface waters and sulphate reducing bacteria (Desulphovibrio desulphuricans) in the brackish water

Fused Deposition of Ceramics: Progress Towards a Robust and Controlled Process for Commercialization

The feasibility of using the Fused Deposition ofCeramics (FDC) process to rapidly fabricate functional quality advanced ceramic components has been demonstratedl - 5 . This direct manufacturing technique, by eliminating the need for costly tooling, dramatically reduces functional prototype development time. This makes it suitable for small quantity production runs and complex parts. The move from 'feasibility" to a robust, reliable commercial fabrication tool requires that every aspect ofthe manufacturing be understood and brought under control. An overview ofthe five basic process steps in FDC: batch compounding, filament fabrication, fused deposition, binder burnout and sintering will be presented in light ofthis drive toward a robust process. Tools such as Statistical Process Control and Experimental Design techniques are being used to monitor, improve, and stabilize each step and sub-process. Hardware and software modifications have been made to the FD machine to effect the required changes. This paper will identify the remaining technical barriers to commercialization and our progress in addressing these issues.Mechanical Engineerin

Statistical methodologies to pool across multiple intervention studies

Combining and analyzing data from heterogeneous randomized controlled trials of complex multiple-component intervention studies, or discussing them in a systematic review, is not straightforward. The present article describes certain issues to be considered when combining data across studies, based on discussions in an NIH-sponsored workshop on pooling issues across studies in consortia (see Belle et al. in Psychol Aging, 18(3):396-405, 2003). Several statistical methodologies are described and their advantages and limitations are explored. Whether weighting the different studies data differently, or via employing random effects, one must recognize that different pooling methodologies may yield different results. Pooling can be used for comprehensive exploratory analyses of data from RCTs and should not be viewed as replacing the standard analysis plan for each study. Pooling may help to identify intervention components that may be more effective especially for subsets of participants with certain behavioral characteristics. Pooling, when supported by statistical tests, can allow exploratory investigation of potential hypotheses and for the design of future interventions

Miaolingian transgression and the <i>Oryctocephalus indicus</i> biozone in the Sumna Valley (Spiti), Himalaya, India

The Oryctocephalus indicus biozone (Wuliuan, Miaolingian) is recognised in the Sumna Valley, in the southeastern part of the Spiti region in the Himalaya, based on the first appearance datum and last appearance datum of Oryctocephalus indicus. The biozone is approximately 5.6 m thick (17.8–23.4 m), and it contains the trilobites Oryctocephalus indicus, Pagetia significans and Kunmingaspis pervulgata. Comparative studies of the lithological variations across the Cambrian Series 2–Wuliuan (Miaolingian) transition in the Parahio and Sumna valleys (southeastern part of the Spiti region) show that the Wuliuan (Miaolingian) deposits transgressed over the undulatory surface of Cambrian Series 2. The uppermost part of the Cambrian Series 2 deposits in the southeastern part of the Spiti region is characterised by a reddish-brown ferruginous, very coarse grained sandstone unit, which indicates a diastem prior to the Wuliuan (Miaolingian) transgression

Topological (Sliced) Doping of a 3D Peierls System: Predicted Structure of Doped BaBiO3

At hole concentrations below x=0.4, Ba_(1-x)K_xBiO_3 is non-metallic. At x=0, pure BaBiO3 is a Peierls insulator. Very dilute holes create bipolaronic point defects in the Peierls order parameter. Here we find that the Rice-Sneddon version of Peierls theory predicts that more concentrated holes should form stacking faults (two-dimensional topological defects, called slices) in the Peierls order parameter. However, the long-range Coulomb interaction, left out of the Rice-Sneddon model, destabilizes slices in favor of point bipolarons at low concentrations, leaving a window near 30% doping where the sliced state is marginally stable.Comment: 6 pages with 5 embedded postscript figure